An elementary proof of Nagel-Schenzel formula

Abstract

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼=  H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.